The mating season for coyotes has now begun, which means we'll be seeing more of them in the months ahead—including right here in the city.

At about 11:30 in the morning this past October 18, a worker at a middle school in Mattapan called the police to report the presence of a coyote near the building. Officers and animal-control specialists rushed to the scene; administrators put the school into lockdown mode; and at least two TV stations hastily dispatched helicopters to track the action from above. A joker on Twitter, watching the live video feed, even began tweeting mock taunts from the coyote to its pursuers as the search for it got under way. The animal was finally caught after an hour-long chase, and the whole episode wound down by early afternoon. A rush of stories followed, not only on local TV and radio but also in the Globe and the Herald.

Expect similar episodes of hysteria in the months ahead. That’s because January typically marks the beginning of mating season for coyotes, a period when they start establishing their territory and make themselves more visible to us than usual. But more sightings don’t necessarily mean an invasion is under way. The eastern coyote actually moved into Massachusetts in the 1950s and has long had a well-established presence all over the state. The Massachusetts Division of Fisheries and Wildlife estimates that some 10,000 coyotes live here, which means we’re all living with them, even in Boston. Last year alone, state wildlife officials captured one in Beacon Hill and another in the Financial District.

The good news is that we don’t need to be afraid of coyotes—although we do need to think twice about letting our pets roam free during the winter months, when coyotes are hungriest. It’s true that one of the animals did bite a young girl in Haverhill last January, but that was only the fifth such episode since the 1950s. By that measure, dogs are vastly more dangerous.

So what should you do if you encounter a coyote? John Maguranis, the animal-control officer in Belmont, recommends approaching it quickly, maintaining eye contact, and affecting a threatening posture. In other words, wave your arms, shout, and carry on like a madman. In the rare cases when that doesn’t work, you may be dealing with a coyote that’s been habituated to people—but just keep at it, and you should be able to chase the animal away.